w^2-21w+44=0

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Solution for w^2-21w+44=0 equation: 


Simplifying
w2 + -21w + 44 = 0

Reorder the terms:
44 + -21w + w2 = 0

Solving
44 + -21w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + -21w + -44 + w2 = 0 + -44

Reorder the terms:
44 + -44 + -21w + w2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -21w + w2 = 0 + -44
-21w + w2 = 0 + -44

Combine like terms: 0 + -44 = -44
-21w + w2 = -44

The w term is -21w.  Take half its coefficient (-10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
-21w + 110.25 + w2 = -44 + 110.25

Reorder the terms:
110.25 + -21w + w2 = -44 + 110.25

Combine like terms: -44 + 110.25 = 66.25
110.25 + -21w + w2 = 66.25

Factor a perfect square on the left side:
(w + -10.5)(w + -10.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(w + -10.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
w + -10.5 = 8.139410298

Simplifying
w + -10.5 = 8.139410298

Reorder the terms:
-10.5 + w = 8.139410298

Solving
-10.5 + w = 8.139410298

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '10.5' to each side of the equation.
-10.5 + 10.5 + w = 8.139410298 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + w = 8.139410298 + 10.5
w = 8.139410298 + 10.5

Combine like terms: 8.139410298 + 10.5 = 18.639410298
w = 18.639410298

Simplifying
w = 18.639410298


Subproblem 2
w + -10.5 = -8.139410298

Simplifying
w + -10.5 = -8.139410298

Reorder the terms:
-10.5 + w = -8.139410298

Solving
-10.5 + w = -8.139410298

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '10.5' to each side of the equation.
-10.5 + 10.5 + w = -8.139410298 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + w = -8.139410298 + 10.5
w = -8.139410298 + 10.5

Combine like terms: -8.139410298 + 10.5 = 2.360589702
w = 2.360589702

Simplifying
w = 2.360589702


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {18.639410298, 2.360589702}

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